Prepare the Apples: Start by peeling and coring the apple. Slice it into thin rings, about 1/4-inch thick. To prevent the apple slices from browning, toss them in a little lime or lemon juice and set them aside.

Make the Batter: In a mixing bowl, whisk together the egg, sugar, and vanilla sugar until well combined. Add the yogurt, milk, and rum, and continue to whisk until the mixture is smooth. In a separate bowl, mix the flour, baking powder, and salt. Gradually add the dry ingredients to the wet ingredients, stirring until a smooth batter forms. The batter should be thick enough to coat the apple slices but still pourable.

Coat the Apples: Dip each apple slice into the batter, making sure it's fully coated. Let any excess batter drip off before placing the slices into the hot oil.

Fry the Fritters: Heat the oil in a deep frying pan or pot to about 350°F (175°C). Carefully add the battered apple slices to the hot oil, frying a few at a time to avoid overcrowding. Fry each side for about 2-3 minutes, or until golden brown. Use a slotted spoon to remove the fritters from the oil and place them on a paper towel-lined plate to drain any excess oil.

Serve: Once all the fritters are cooked, you can serve them warm, dusted with powdered sugar or with a drizzle of honey. They’re also delicious with a scoop of vanilla ice cream or a dollop of whipped cream.